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<H1>BOI 98 Day 1 Problem 1</H1>
<H1>Meeting</H1>
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<P>Two diplomats, on a mission from their respective countries, are in
the same city to engage in negotiations. They are staying in different
hotels. They would like to arrange a rendezvous with the following conditions.
They are supposed to leave their hotels exactly at the same time and arrive
at some meeting point exactly at the same time. They walk at the same speed.
So it is assured that both parties get an equal treatment: they walk the
same distance and no one will be standing alone at the meeting point waiting
for the other. The city map will be given to you: On the map streets are
shown along with the distances between any two points connected by a street;
points where the two hotels are located are marked. It is possible to reach
from any point of interest to any other. Your task is to find a place in
town which could be a meeting point and specify the two routes to this
point. The point you find must enable the meeting to start at the earliest
possible time (with respect to the departure time from their hotels). Also,
no one must pass through the same point twice. Moreover, the two diplomats
must follow disjoint routes (i.e. routes that do not have a point in common
except the meeting point).You are assured that at least one such meeting
point exists.

<H2>Input</H2>
The points of interest on the map are numbered 1 through P consecutively
(1 &lt;= P &lt;= 200). If points i and j are connected by a street, the distance
between these points, D<sub>i,j</sub> will be an integer (1 &lt;= D<sub>i,j</sub>&lt;= 10). The first
line of the input file contains three integers, each separated by a blank.
The first integer, call it L, is the number of the lines that follow (L
 &lt;=500). The second and third integers designate the locations of the hotels
the two diplomats are staying. Each of the L lines has three numbers, each
separated by blanks. These numbers are i, j and D<sub>i,j</sub>-in left to right
order. These three numbers represent two points of interest, i and j, connected
by a street such that their distance along this street is D<sub>i,j</sub>. Notice
that the order of i and j is not important. Moreover, there will not be
another line with the same i and j. The input will be a text file named
meet.inp.

<H2>Output</H2>
Your output must be a text file to be named meet.out. The output must
consist of two lines each holding a route for a diplomat. The route for
a diplomat is a sequence of integers, each separated by a blank, where
each integer designates a point along the route. The first point must be
the hotel and the last point must be the meeting point. The ordering of
the two lines is not important.

<H2>Sample Input</H2>
<pre>
22 1 8
1 13 2
1 2 1
2 6 4
2 3 1
3 4 1
3 5 1
4 5 1
4 6 2
5 7 2
6 7 3
5 14 2
7 8 3
7 14 2
13 14 4
13 12 3
12 14 4
12 11 2
11 14 3
11 10 2
10 8 1
10 9 2
9 8 2
</PRE>

<h2>Sample Output</h2>
<pre>
1 2 3 5 14
8 7 14
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<h2>Note</h2>
Here is the picture of the sample input:<br>
<center><img src="image/293.gif" HEIGHT=224 WIDTH=280></center>

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